*math stuff*
Seems the smart move would have been a formal consult / audit of the scoring system from a pro! Hindsight and all.
As an auditor by profession, I do maintain the view that audit can be helpful!
In fairness, I probably would have commented at the start (early enough for you to do something about it) if I'd realised how narrow the quality scores would likely end up being, but I was more focused on trying unsuccessfully to qualify and didn't realise until round 1 was nearly over.
I think if you'd used a 1.0-10.0 stack ranking system for scoring quality, that would have achieved what you were going for and been a genuine half and half weighting.
The real dick move would be re-score rounds 1-4. That would REALLY chafe Tims chaps!!
Considering his current quality-only placement, that would be brutal.
Anyway I think your amendment works quite well. It won't shift the priority for everyone, but it does create an incentive for those who are unlikely to catch up on hangman-related scores to prioritise quality and go for that opportunity.